Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish. Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group:

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish. The composition parameters (\(P_{(pelagic)ayu}\), \(P_{(black|pelagic)ayu}\), \(P_{(yelloweye|non-pelagic)ayu}\)) were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping (pelagic or yelloweye), \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases calculated from the sum of the user group releases. The proportion of total rockfish harvested by user group, \(pH_{ayu}\), was assumed to be the mean of \(pH_{(pelagic)ayu}\), \(pH_{(yelloweye)ayu}\) and \(pH_{(nonpel-nonYE)ayu}\) weighted by the relative harvest \(H_{(comp)ayu}\) such that

\[\begin{equation} R_{ayu}~=~ \frac{\sum ({H_{(comp)ayu} * pH_{(comp)ayu})}}{\sum {H_{(comp)ayu}}} \end{equation}\]

The proportion harvest parameters \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{ayuc})~=~\beta1_{(pH)ayuc} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc}))) + \beta34_{(pH)ayuc}} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \end{equation}\]

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modelled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \end{equation}\]

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modelled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

**Figure 13.**- Annual proportion of all rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of all rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_yellow 2 42.713444
sd_comp 1 3.759211
beta1_yellow 3 3.735961
beta2_yellow 5 2.883936
beta4_yellow 1 2.124586
beta3_pH 1 1.476525
beta1_pelagic 2 1.324125
beta0_pelagic 3 1.296574
beta2_pH 2 1.275550
parameter n badRhat_avg
tau_beta0_pelagic 1 1.224420
beta3_pelagic 1 1.216398
beta0_yellow 2 1.187192
beta0_pH 2 1.183596
beta1_pH 3 1.179332
beta2_pelagic 2 1.153876
beta0_black 1 1.119605
beta1_black 1 1.111821
Table 2. Summary of unconverged parameters by area
afognak CI CSEO EWYKT NG PWSI WKMA
beta0_black 0 0 1 0 0 0 0
beta0_pelagic 1 0 1 0 1 0 0
beta0_pH 0 0 1 0 0 0 0
beta0_yellow 0 0 0 0 0 1 1
beta1_black 0 0 1 0 0 0 0
beta1_pelagic 0 0 1 0 1 0 0
beta1_pH 0 0 1 0 0 0 0
beta1_yellow 0 0 1 1 0 1 0
beta2_pelagic 1 0 1 0 0 0 0
beta2_pH 0 0 1 0 0 0 0
beta2_yellow 1 0 1 1 0 1 1
beta3_pelagic 0 0 1 0 0 0 0
beta3_pH 0 0 1 0 0 0 0
beta3_yellow 0 0 1 1 0 0 0
beta4_yellow 0 0 1 0 0 0 0
sd_comp 0 0 0 0 0 0 0
tau_beta0_pelagic 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.158 0.070 -0.285 -0.160 -0.012
mu_bc_H[2] -0.122 0.037 -0.190 -0.124 -0.041
mu_bc_H[3] -0.461 0.068 -0.590 -0.463 -0.325
mu_bc_H[4] -1.188 0.224 -1.645 -1.179 -0.772
mu_bc_H[5] 0.583 0.679 -0.305 0.489 2.067
mu_bc_H[6] -2.236 0.317 -2.858 -2.241 -1.602
mu_bc_H[7] -0.483 0.113 -0.714 -0.480 -0.270
mu_bc_H[8] 0.140 0.377 -0.506 0.117 0.930
mu_bc_H[9] -0.323 0.131 -0.582 -0.323 -0.069
mu_bc_H[10] -0.128 0.067 -0.252 -0.129 0.011
mu_bc_H[11] -0.129 0.035 -0.200 -0.129 -0.060
mu_bc_H[12] -0.266 0.110 -0.511 -0.259 -0.069
mu_bc_H[13] -0.152 0.077 -0.302 -0.152 -0.004
mu_bc_H[14] -0.326 0.096 -0.521 -0.324 -0.140
mu_bc_H[15] -0.361 0.047 -0.450 -0.362 -0.268
mu_bc_H[16] -0.311 0.378 -0.965 -0.343 0.525
mu_bc_R[1] 1.896 0.779 -0.012 1.999 3.082
mu_bc_R[2] 1.240 0.721 -0.338 1.296 2.485
mu_bc_R[3] 1.494 0.649 -0.108 1.615 2.453
mu_bc_R[4] -0.046 0.968 -2.098 0.012 1.827
mu_bc_R[5] 1.641 0.978 -0.056 1.544 3.898
mu_bc_R[6] 0.635 0.608 -0.724 0.688 1.714
mu_bc_R[7] 1.443 1.102 -0.920 1.524 3.001
mu_bc_R[8] 2.099 0.658 0.485 2.185 3.096
mu_bc_R[9] 2.308 1.064 0.076 2.421 3.927
mu_bc_R[10] 2.052 1.338 -0.580 1.998 4.461
mu_bc_R[11] 1.131 0.440 -0.211 1.195 1.753
mu_bc_R[12] -0.520 0.560 -1.560 -0.547 0.604
mu_bc_R[13] 0.420 0.387 -0.390 0.445 1.124
mu_bc_R[14] 0.574 0.374 -0.123 0.568 1.359
mu_bc_R[15] 0.489 0.219 0.108 0.473 0.955
mu_bc_R[16] 1.215 0.400 0.229 1.263 1.831
tau_pH[1] 98241.487 1846011.263 66.813 641.473 154581.545
tau_pH[2] 2.654 0.328 2.066 2.631 3.367
tau_pH[3] 3.274 0.538 2.022 3.303 4.249
beta0_pH[1,1] 1.950 1.002 -0.243 2.014 3.667
beta0_pH[2,1] 2.107 0.916 0.233 2.129 3.812
beta0_pH[3,1] 2.078 0.981 -0.099 2.122 3.880
beta0_pH[4,1] 1.751 1.394 -1.611 1.939 3.897
beta0_pH[5,1] 2.207 1.594 -0.313 1.999 5.941
beta0_pH[6,1] 2.460 1.917 -0.238 2.045 6.924
beta0_pH[7,1] 2.354 1.942 -0.656 2.108 6.258
beta0_pH[8,1] 1.496 1.069 -0.707 1.541 3.567
beta0_pH[9,1] 2.141 1.584 -0.626 2.035 5.202
beta0_pH[10,1] 2.124 1.452 -0.606 2.028 5.039
beta0_pH[11,1] -1.004 0.615 -2.321 -0.966 0.101
beta0_pH[12,1] -0.935 0.693 -2.420 -0.921 0.398
beta0_pH[13,1] -0.984 0.606 -2.260 -0.959 0.161
beta0_pH[14,1] -1.007 0.698 -2.475 -0.992 0.347
beta0_pH[15,1] -1.108 0.612 -2.490 -1.049 -0.069
beta0_pH[16,1] -1.187 0.644 -2.623 -1.112 -0.113
beta0_pH[1,2] 2.376 0.219 1.963 2.375 2.808
beta0_pH[2,2] 2.626 0.326 1.926 2.669 3.145
beta0_pH[3,2] 2.344 0.259 1.792 2.355 2.824
beta0_pH[4,2] 2.464 0.297 1.853 2.501 2.930
beta0_pH[5,2] 3.058 0.980 1.601 2.905 5.314
beta0_pH[6,2] 2.675 0.284 2.102 2.691 3.150
beta0_pH[7,2] 1.862 0.419 0.607 1.930 2.269
beta0_pH[8,2] 2.630 0.438 1.497 2.718 3.095
beta0_pH[9,2] 2.629 0.520 1.731 2.580 3.534
beta0_pH[10,2] 2.910 0.720 1.366 3.013 3.915
beta0_pH[11,2] -4.806 0.324 -5.482 -4.799 -4.199
beta0_pH[12,2] -4.681 0.439 -5.601 -4.650 -3.881
beta0_pH[13,2] -4.478 0.381 -5.205 -4.490 -3.702
beta0_pH[14,2] -5.387 0.450 -6.279 -5.382 -4.543
beta0_pH[15,2] -4.146 0.336 -4.786 -4.150 -3.477
beta0_pH[16,2] -4.450 0.335 -5.110 -4.459 -3.790
beta0_pH[1,3] 1.164 0.301 0.540 1.188 1.630
beta0_pH[2,3] 1.497 0.562 0.064 1.555 2.374
beta0_pH[3,3] 1.926 0.533 0.792 1.981 2.732
beta0_pH[4,3] 1.859 0.772 0.218 1.832 3.015
beta0_pH[5,3] 0.286 0.790 -1.419 0.365 1.302
beta0_pH[6,3] 0.078 0.896 -1.952 0.262 1.000
beta0_pH[7,3] 0.390 0.427 -0.684 0.470 0.951
beta0_pH[8,3] 0.313 0.204 -0.105 0.322 0.686
beta0_pH[9,3] 0.350 0.474 -0.735 0.399 1.116
beta0_pH[10,3] 0.285 0.396 -0.738 0.349 0.864
beta0_pH[11,3] -0.138 0.496 -1.006 -0.174 1.264
beta0_pH[12,3] -3.426 0.470 -4.409 -3.420 -2.502
beta0_pH[13,3] 0.077 0.353 -0.685 0.097 0.705
beta0_pH[14,3] -0.451 0.270 -1.012 -0.439 0.046
beta0_pH[15,3] -0.633 0.313 -1.236 -0.637 -0.045
beta0_pH[16,3] 0.122 0.286 -0.514 0.142 0.613
beta1_pH[1,1] 1.917 0.691 1.029 1.759 3.707
beta1_pH[2,1] 0.959 0.460 0.469 0.864 2.087
beta1_pH[3,1] 1.675 0.883 0.498 1.474 3.902
beta1_pH[4,1] 1.893 1.578 0.133 1.422 6.226
beta1_pH[5,1] 2.424 1.469 0.260 2.172 6.165
beta1_pH[6,1] 4.595 2.104 0.734 4.648 8.689
beta1_pH[7,1] 3.129 1.877 0.164 3.113 6.940
beta1_pH[8,1] 2.151 0.628 1.113 2.092 3.503
beta1_pH[9,1] 1.444 0.897 0.166 1.361 3.668
beta1_pH[10,1] 1.045 0.248 0.644 1.022 1.606
beta1_pH[11,1] 3.988 0.767 1.894 4.018 5.419
beta1_pH[12,1] 1.792 0.539 0.983 1.718 3.076
beta1_pH[13,1] 2.808 0.662 1.765 2.713 4.299
beta1_pH[14,1] 2.434 0.503 1.581 2.389 3.570
beta1_pH[15,1] 2.666 0.624 1.682 2.583 4.107
beta1_pH[16,1] 4.898 0.873 3.326 4.829 6.795
beta1_pH[1,2] 1.342 0.561 0.444 1.299 2.368
beta1_pH[2,2] 1.187 1.248 0.080 0.772 5.109
beta1_pH[3,2] 1.325 0.318 0.713 1.324 1.981
beta1_pH[4,2] 1.665 1.632 0.125 1.007 6.197
beta1_pH[5,2] 3.256 1.984 0.301 2.997 7.851
beta1_pH[6,2] 1.929 1.021 0.472 1.756 4.628
beta1_pH[7,2] 2.411 2.234 0.056 1.545 7.679
beta1_pH[8,2] 1.451 1.563 0.046 0.848 5.873
beta1_pH[9,2] 1.485 0.958 0.145 1.361 4.368
beta1_pH[10,2] 1.568 1.226 0.137 1.292 4.983
beta1_pH[11,2] 6.745 0.359 6.069 6.738 7.476
beta1_pH[12,2] 6.777 0.566 5.771 6.735 7.992
beta1_pH[13,2] 7.036 0.438 6.149 7.032 7.913
beta1_pH[14,2] 7.325 0.488 6.398 7.318 8.293
beta1_pH[15,2] 6.696 0.374 5.965 6.700 7.414
beta1_pH[16,2] 7.187 0.375 6.446 7.189 7.901
beta1_pH[1,3] 2.022 0.486 1.283 1.975 3.142
beta1_pH[2,3] 1.152 0.735 0.184 1.019 3.078
beta1_pH[3,3] 1.107 0.737 0.175 0.986 3.202
beta1_pH[4,3] 1.536 1.106 0.127 1.358 4.492
beta1_pH[5,3] 2.149 1.698 0.105 1.763 6.478
beta1_pH[6,3] 2.007 1.809 0.064 1.451 6.736
beta1_pH[7,3] 1.541 1.716 0.051 0.798 6.347
beta1_pH[8,3] 2.734 0.366 2.025 2.737 3.465
beta1_pH[9,3] 1.527 0.946 0.194 1.427 3.926
beta1_pH[10,3] 3.026 0.524 2.198 2.966 4.257
beta1_pH[11,3] 2.815 0.709 0.591 2.903 3.849
beta1_pH[12,3] 6.744 0.525 5.750 6.737 7.817
beta1_pH[13,3] 2.066 0.401 1.338 2.054 2.897
beta1_pH[14,3] 2.987 0.330 2.356 2.977 3.664
beta1_pH[15,3] 2.575 0.353 1.899 2.560 3.284
beta1_pH[16,3] 1.718 0.332 1.101 1.700 2.406
beta2_pH[1,1] 0.801 1.223 0.099 0.330 4.716
beta2_pH[2,1] 1.921 1.887 0.121 1.247 6.761
beta2_pH[3,1] 2.910 2.095 0.103 2.553 7.684
beta2_pH[4,1] 0.234 3.303 -5.923 0.558 6.691
beta2_pH[5,1] 2.626 2.448 -2.257 2.360 7.814
beta2_pH[6,1] 2.848 2.145 0.043 2.555 7.656
beta2_pH[7,1] -1.061 3.742 -7.192 -1.847 6.562
beta2_pH[8,1] 2.215 1.916 0.190 1.535 7.028
beta2_pH[9,1] 2.442 2.608 -3.343 2.325 7.906
beta2_pH[10,1] 2.408 1.813 0.328 1.934 6.975
beta2_pH[11,1] 0.641 0.522 0.289 0.539 1.657
beta2_pH[12,1] 2.251 1.958 0.126 1.656 7.190
beta2_pH[13,1] 1.467 1.706 0.180 0.646 6.158
beta2_pH[14,1] 3.592 1.985 0.708 3.215 8.283
beta2_pH[15,1] 1.962 1.850 0.191 1.266 6.680
beta2_pH[16,1] 0.297 0.156 0.156 0.276 0.542
beta2_pH[1,2] 2.175 2.036 -2.365 1.877 6.446
beta2_pH[2,2] -1.127 2.880 -7.113 -0.796 4.687
beta2_pH[3,2] -3.039 1.882 -7.560 -2.602 -0.597
beta2_pH[4,2] -2.818 2.332 -7.745 -2.618 1.323
beta2_pH[5,2] 0.868 2.871 -5.704 0.977 6.151
beta2_pH[6,2] -2.572 2.132 -7.393 -2.150 -0.115
beta2_pH[7,2] -2.929 2.561 -8.087 -2.826 2.541
beta2_pH[8,2] -1.635 3.119 -7.627 -1.788 4.867
beta2_pH[9,2] -2.681 2.526 -7.781 -2.597 2.878
beta2_pH[10,2] -0.276 3.387 -6.928 0.264 5.793
beta2_pH[11,2] -5.209 1.678 -9.269 -4.971 -2.616
beta2_pH[12,2] -1.191 0.795 -3.350 -0.971 -0.497
beta2_pH[13,2] -2.406 1.050 -5.223 -2.145 -1.164
beta2_pH[14,2] -3.479 1.565 -7.365 -3.122 -1.450
beta2_pH[15,2] -4.920 1.667 -8.823 -4.632 -2.378
beta2_pH[16,2] -5.652 1.687 -9.312 -5.409 -3.004
beta2_pH[1,3] 2.867 1.807 0.308 2.592 7.135
beta2_pH[2,3] 1.751 2.144 -2.411 1.345 6.701
beta2_pH[3,3] -1.240 3.148 -6.716 -1.666 5.693
beta2_pH[4,3] 1.312 2.725 -5.139 1.313 6.482
beta2_pH[5,3] -0.248 3.175 -6.462 -0.335 6.172
beta2_pH[6,3] 0.368 3.197 -5.960 0.502 6.399
beta2_pH[7,3] -0.317 3.211 -6.531 -0.097 6.001
beta2_pH[8,3] 4.577 1.993 1.315 4.401 8.937
beta2_pH[9,3] 1.858 2.646 -4.183 1.837 6.974
beta2_pH[10,3] 1.538 1.370 0.370 1.019 5.585
beta2_pH[11,3] -1.070 1.774 -4.406 -1.133 3.741
beta2_pH[12,3] -1.209 0.324 -1.977 -1.161 -0.758
beta2_pH[13,3] -2.377 1.528 -6.397 -1.948 -0.655
beta2_pH[14,3] -2.470 1.339 -6.168 -2.119 -0.895
beta2_pH[15,3] -2.284 1.444 -6.326 -1.821 -0.749
beta2_pH[16,3] -2.567 1.543 -6.486 -2.178 -0.669
beta3_pH[1,1] 35.632 2.751 31.259 35.237 42.100
beta3_pH[2,1] 36.171 1.971 32.574 36.087 40.954
beta3_pH[3,1] 33.398 2.313 26.645 33.879 35.883
beta3_pH[4,1] 31.898 7.545 20.195 33.805 42.810
beta3_pH[5,1] 36.844 5.794 22.074 38.808 43.750
beta3_pH[6,1] 32.922 6.537 19.570 35.849 40.330
beta3_pH[7,1] 26.304 7.377 19.350 21.142 42.007
beta3_pH[8,1] 32.193 2.260 28.300 32.296 35.808
beta3_pH[9,1] 29.185 4.247 21.030 28.854 41.013
beta3_pH[10,1] 34.199 1.812 29.435 34.671 36.527
beta3_pH[11,1] 29.271 0.923 27.352 29.288 31.367
beta3_pH[12,1] 30.710 2.482 26.600 30.221 35.886
beta3_pH[13,1] 32.840 1.422 30.608 32.642 35.944
beta3_pH[14,1] 30.493 0.795 29.253 30.535 31.648
beta3_pH[15,1] 32.224 1.813 28.580 32.364 35.549
beta3_pH[16,1] 32.132 1.385 29.342 32.148 34.893
beta3_pH[1,2] 40.216 3.565 25.765 40.757 43.504
beta3_pH[2,2] 30.378 6.695 19.580 29.486 42.331
beta3_pH[3,2] 41.886 0.946 39.982 41.959 43.598
beta3_pH[4,2] 33.316 8.405 20.184 36.780 43.233
beta3_pH[5,2] 30.040 6.357 19.911 29.587 42.652
beta3_pH[6,2] 34.556 2.923 26.579 35.194 38.424
beta3_pH[7,2] 26.529 6.146 19.368 25.347 38.757
beta3_pH[8,2] 29.267 6.370 19.658 28.211 41.975
beta3_pH[9,2] 38.274 7.845 20.417 43.125 43.969
beta3_pH[10,2] 30.007 6.649 19.814 28.728 41.865
beta3_pH[11,2] 43.358 0.137 43.130 43.345 43.666
beta3_pH[12,2] 42.894 0.337 42.156 42.926 43.483
beta3_pH[13,2] 43.719 0.165 43.354 43.742 43.975
beta3_pH[14,2] 43.252 0.149 42.977 43.244 43.558
beta3_pH[15,2] 43.444 0.155 43.162 43.442 43.749
beta3_pH[16,2] 43.464 0.148 43.202 43.458 43.764
beta3_pH[1,3] 40.129 0.886 38.474 40.129 41.778
beta3_pH[2,3] 32.152 4.227 21.640 32.419 40.723
beta3_pH[3,3] 35.930 7.238 20.798 40.639 43.391
beta3_pH[4,3] 27.839 4.612 19.636 28.140 38.486
beta3_pH[5,3] 30.675 6.361 19.841 30.522 42.790
beta3_pH[6,3] 31.584 6.747 19.931 31.624 42.756
beta3_pH[7,3] 28.097 6.284 19.513 27.218 41.593
beta3_pH[8,3] 41.480 0.288 40.904 41.483 42.023
beta3_pH[9,3] 31.981 4.690 19.915 33.400 40.492
beta3_pH[10,3] 36.717 0.984 34.506 36.743 38.522
beta3_pH[11,3] 40.236 4.550 24.054 41.501 42.845
beta3_pH[12,3] 42.594 0.280 42.035 42.593 43.113
beta3_pH[13,3] 42.207 0.754 40.817 42.155 43.683
beta3_pH[14,3] 41.100 0.419 40.193 41.118 41.889
beta3_pH[15,3] 41.999 0.632 40.786 41.986 43.251
beta3_pH[16,3] 41.596 0.845 40.025 41.536 43.311
beta0_pelagic[1] 1.369 0.630 0.095 1.426 2.307
beta0_pelagic[2] 1.146 0.432 0.008 1.292 1.629
beta0_pelagic[3] 0.080 0.419 -1.138 0.182 0.580
beta0_pelagic[4] 0.254 0.327 -0.567 0.299 0.787
beta0_pelagic[5] 0.519 0.496 -0.766 0.634 1.204
beta0_pelagic[6] 0.519 0.474 -0.624 0.582 1.247
beta0_pelagic[7] 1.462 0.177 1.107 1.471 1.772
beta0_pelagic[8] 1.624 0.249 0.981 1.662 1.933
beta0_pelagic[9] 1.778 0.540 0.434 1.902 2.521
beta0_pelagic[10] 2.174 0.585 0.515 2.381 2.794
beta0_pelagic[11] -1.049 0.818 -2.859 -0.800 -0.017
beta0_pelagic[12] 1.645 0.148 1.349 1.647 1.932
beta0_pelagic[13] 0.276 0.201 -0.196 0.293 0.625
beta0_pelagic[14] -0.230 0.278 -0.844 -0.204 0.235
beta0_pelagic[15] -0.315 0.125 -0.564 -0.314 -0.070
beta0_pelagic[16] -0.217 0.337 -0.980 -0.164 0.303
beta1_pelagic[1] 1.131 0.972 0.052 0.949 4.078
beta1_pelagic[2] 0.655 0.833 0.015 0.310 3.043
beta1_pelagic[3] 1.092 0.726 0.402 0.865 3.313
beta1_pelagic[4] 0.988 0.377 0.392 0.933 1.964
beta1_pelagic[5] 0.650 0.692 0.018 0.456 2.313
beta1_pelagic[6] 1.278 0.602 0.421 1.180 2.854
beta1_pelagic[7] 2.127 1.826 0.142 1.412 6.558
beta1_pelagic[8] 1.172 1.484 0.026 0.562 5.400
beta1_pelagic[9] 1.464 0.722 0.508 1.320 3.368
beta1_pelagic[10] 0.838 1.037 0.024 0.421 4.002
beta1_pelagic[11] 4.734 1.363 2.656 4.447 7.997
beta1_pelagic[12] 3.022 0.325 2.393 3.012 3.665
beta1_pelagic[13] 2.338 0.442 1.634 2.303 3.386
beta1_pelagic[14] 3.990 0.607 2.957 3.952 5.266
beta1_pelagic[15] 2.465 0.253 1.966 2.470 2.964
beta1_pelagic[16] 3.772 0.685 2.669 3.690 5.342
beta2_pelagic[1] 2.045 2.244 -2.280 1.705 7.086
beta2_pelagic[2] 0.972 2.448 -4.623 0.540 6.152
beta2_pelagic[3] 1.612 1.779 0.057 0.817 6.053
beta2_pelagic[4] 2.257 1.789 0.163 1.781 6.622
beta2_pelagic[5] 0.507 3.214 -5.813 0.667 6.508
beta2_pelagic[6] 2.096 1.914 0.104 1.572 6.724
beta2_pelagic[7] -1.896 1.754 -6.040 -1.439 -0.025
beta2_pelagic[8] -2.100 2.350 -6.513 -2.458 3.734
beta2_pelagic[9] 1.810 1.929 0.072 1.027 6.595
beta2_pelagic[10] 1.113 2.555 -4.783 0.768 6.664
beta2_pelagic[11] 0.148 0.057 0.066 0.140 0.284
beta2_pelagic[12] 1.053 0.360 0.540 0.989 1.831
beta2_pelagic[13] 0.707 0.617 0.198 0.532 2.297
beta2_pelagic[14] 0.304 0.106 0.162 0.283 0.571
beta2_pelagic[15] 1.805 0.871 0.834 1.587 4.183
beta2_pelagic[16] 0.344 0.207 0.149 0.293 0.855
beta3_pelagic[1] 24.964 4.236 19.977 23.248 35.866
beta3_pelagic[2] 28.734 4.959 19.550 28.889 38.066
beta3_pelagic[3] 30.339 3.066 24.526 30.318 37.689
beta3_pelagic[4] 26.117 2.035 22.597 26.083 31.511
beta3_pelagic[5] 28.205 4.914 20.498 27.651 38.363
beta3_pelagic[6] 30.613 3.358 25.118 30.447 37.720
beta3_pelagic[7] 26.978 3.165 20.068 27.040 32.861
beta3_pelagic[8] 26.457 4.800 20.239 25.967 37.039
beta3_pelagic[9] 31.789 3.878 23.354 32.852 37.102
beta3_pelagic[10] 27.623 5.112 19.323 27.504 37.682
beta3_pelagic[11] 37.456 2.783 30.711 37.905 41.578
beta3_pelagic[12] 41.884 0.125 41.548 41.923 41.997
beta3_pelagic[13] 40.940 0.909 38.555 41.177 41.961
beta3_pelagic[14] 40.674 1.071 38.010 40.932 41.956
beta3_pelagic[15] 41.836 0.161 41.383 41.886 41.996
beta3_pelagic[16] 40.646 1.251 37.287 41.015 41.962
mu_beta0_pelagic[1] 0.627 0.783 -1.018 0.684 1.917
mu_beta0_pelagic[2] 1.299 0.496 0.232 1.339 2.150
mu_beta0_pelagic[3] -0.007 0.622 -1.342 0.051 1.007
tau_beta0_pelagic[1] 6.744 20.615 0.072 1.516 65.974
tau_beta0_pelagic[2] 2.335 3.298 0.202 1.476 10.192
tau_beta0_pelagic[3] 1.241 1.007 0.121 0.986 3.922
beta0_yellow[1] -0.472 0.227 -0.980 -0.449 -0.128
beta0_yellow[2] 0.357 0.253 -0.433 0.396 0.697
beta0_yellow[3] -0.435 0.256 -0.901 -0.407 -0.116
beta0_yellow[4] 0.336 0.533 -0.794 0.440 1.086
beta0_yellow[5] -1.714 0.475 -2.582 -1.730 -0.719
beta0_yellow[6] 0.085 0.315 -0.485 0.088 0.692
beta0_yellow[7] 0.615 1.103 -2.483 1.088 1.616
beta0_yellow[8] 0.837 0.405 -0.454 0.914 1.317
beta0_yellow[9] -0.214 0.373 -0.934 -0.222 0.540
beta0_yellow[10] 0.613 0.184 0.251 0.614 0.976
beta0_yellow[11] -4.903 0.114 -4.999 -4.948 -4.582
beta0_yellow[12] -4.871 0.190 -4.999 -4.943 -4.335
beta0_yellow[13] -4.925 0.091 -4.999 -4.959 -4.665
beta0_yellow[14] -4.920 0.099 -4.999 -4.958 -4.641
beta0_yellow[15] -4.904 0.117 -4.999 -4.948 -4.581
beta0_yellow[16] -4.940 0.071 -4.999 -4.966 -4.741
beta1_yellow[1] 0.498 0.637 0.013 0.304 2.132
beta1_yellow[2] 1.326 0.580 0.734 1.187 3.142
beta1_yellow[3] 0.823 0.482 0.357 0.751 1.901
beta1_yellow[4] 2.515 1.188 0.872 2.297 5.084
beta1_yellow[5] 4.289 1.740 1.445 4.046 8.237
beta1_yellow[6] 3.151 1.662 0.780 2.823 7.211
beta1_yellow[7] 2.731 2.051 0.099 2.323 7.454
beta1_yellow[8] 1.934 1.646 0.086 1.423 6.217
beta1_yellow[9] 1.981 0.745 0.647 1.952 3.415
beta1_yellow[10] 2.460 0.553 1.485 2.413 3.594
beta1_yellow[11] 4.406 0.488 3.487 4.602 5.053
beta1_yellow[12] 6.216 1.913 3.348 7.083 8.646
beta1_yellow[13] 3.801 0.181 3.423 3.805 4.153
beta1_yellow[14] 4.718 0.196 4.293 4.731 5.069
beta1_yellow[15] 3.685 0.196 3.249 3.693 4.044
beta1_yellow[16] 4.606 0.180 4.254 4.608 4.956
beta2_yellow[1] -0.902 2.604 -6.230 -0.858 4.659
beta2_yellow[2] -2.080 1.787 -6.420 -1.643 -0.090
beta2_yellow[3] -1.858 1.676 -6.206 -1.398 -0.089
beta2_yellow[4] -0.574 1.123 -4.373 -0.161 -0.052
beta2_yellow[5] -3.301 1.794 -7.529 -3.013 -0.692
beta2_yellow[6] 2.896 1.965 0.178 2.628 7.289
beta2_yellow[7] -1.512 3.559 -7.258 -2.049 5.735
beta2_yellow[8] -2.243 2.513 -6.593 -2.434 3.781
beta2_yellow[9] 2.705 2.171 -2.211 2.492 7.180
beta2_yellow[10] -3.379 1.952 -8.226 -3.060 -0.672
beta2_yellow[11] -1.961 5.420 -8.707 -4.560 7.900
beta2_yellow[12] 1.458 2.334 -0.070 -0.028 7.387
beta2_yellow[13] -3.062 1.239 -6.178 -2.787 -1.406
beta2_yellow[14] -3.943 1.454 -7.522 -3.652 -1.823
beta2_yellow[15] -2.755 1.333 -6.141 -2.430 -1.090
beta2_yellow[16] -6.102 1.452 -9.137 -6.017 -3.557
beta3_yellow[1] 28.343 4.853 19.980 28.246 38.212
beta3_yellow[2] 29.223 1.839 25.407 29.034 33.199
beta3_yellow[3] 31.948 2.116 27.143 31.948 36.048
beta3_yellow[4] 29.749 3.647 22.316 29.736 36.510
beta3_yellow[5] 32.478 1.072 30.465 32.518 34.135
beta3_yellow[6] 38.454 2.255 30.900 38.759 41.073
beta3_yellow[7] 27.172 3.233 21.393 27.024 34.941
beta3_yellow[8] 29.142 3.702 21.672 28.998 35.670
beta3_yellow[9] 36.142 2.618 27.464 36.631 39.288
beta3_yellow[10] 29.210 0.682 27.623 29.307 30.226
beta3_yellow[11] 38.834 6.801 29.024 43.546 43.870
beta3_yellow[12] 32.572 3.607 29.039 31.541 41.238
beta3_yellow[13] 43.818 0.209 43.368 43.831 44.199
beta3_yellow[14] 43.767 0.209 43.343 43.776 44.161
beta3_yellow[15] 43.937 0.240 43.455 43.932 44.449
beta3_yellow[16] 43.611 0.143 43.334 43.617 43.881
mu_beta0_yellow[1] -0.061 0.417 -0.923 -0.058 0.801
mu_beta0_yellow[2] 0.004 0.578 -1.215 0.049 1.074
mu_beta0_yellow[3] -5.322 0.427 -6.379 -5.245 -4.722
tau_beta0_yellow[1] 6.037 11.077 0.245 2.894 35.992
tau_beta0_yellow[2] 0.995 0.819 0.113 0.771 3.057
tau_beta0_yellow[3] 72.493 77.673 3.280 45.355 312.485
beta0_black[1] -0.093 0.145 -0.376 -0.094 0.196
beta0_black[2] 1.681 0.314 0.723 1.750 2.054
beta0_black[3] 1.143 0.379 0.188 1.214 1.527
beta0_black[4] 1.820 0.398 0.640 1.914 2.260
beta0_black[5] 1.373 1.213 -0.714 1.336 3.606
beta0_black[6] 1.380 1.198 -0.786 1.334 3.543
beta0_black[7] 1.370 1.138 -0.881 1.346 3.423
beta0_black[8] 1.116 0.301 0.407 1.156 1.580
beta0_black[9] 1.656 0.493 0.708 1.634 2.527
beta0_black[10] 1.357 0.139 1.090 1.358 1.625
beta0_black[11] 3.271 0.432 1.957 3.351 3.692
beta0_black[12] 4.393 0.185 4.034 4.392 4.760
beta0_black[13] -0.088 0.220 -0.526 -0.085 0.322
beta0_black[14] 1.757 0.671 0.087 1.943 2.596
beta0_black[15] 0.992 0.365 0.017 1.082 1.477
beta0_black[16] 3.281 0.999 0.676 3.593 4.350
beta2_black[1] 3.225 1.674 0.878 2.944 7.092
beta2_black[2] -1.352 2.578 -5.988 -1.203 3.765
beta2_black[3] 0.157 3.140 -5.844 0.128 6.191
beta2_black[4] -1.919 1.737 -6.051 -1.450 -0.058
beta2_black[5] -0.136 3.115 -6.299 -0.157 5.995
beta2_black[6] 0.078 3.130 -5.960 0.188 5.855
beta2_black[7] -0.079 3.117 -6.107 -0.147 5.965
beta2_black[8] -3.158 2.066 -7.679 -2.984 -0.118
beta2_black[9] -1.467 2.539 -6.687 -1.081 4.269
beta2_black[10] -0.894 2.906 -6.506 -1.056 5.575
beta2_black[11] -1.726 2.100 -6.300 -1.447 2.793
beta2_black[12] -3.227 1.744 -7.227 -2.824 -0.842
beta2_black[13] -2.158 1.553 -6.313 -1.678 -0.451
beta2_black[14] -0.868 1.312 -5.107 -0.317 -0.077
beta2_black[15] -1.755 1.938 -6.527 -1.250 0.109
beta2_black[16] 1.998 2.062 -1.200 1.609 6.671
beta3_black[1] 41.831 0.721 40.270 41.944 42.999
beta3_black[2] 30.220 8.047 19.225 30.956 44.962
beta3_black[3] 28.033 7.227 19.197 28.395 44.140
beta3_black[4] 32.789 3.817 21.804 32.909 39.738
beta3_black[5] 31.948 7.314 19.784 31.749 45.046
beta3_black[6] 32.001 7.405 19.769 31.778 45.061
beta3_black[7] 31.521 7.398 19.649 31.177 44.634
beta3_black[8] 28.620 7.842 20.469 23.294 42.878
beta3_black[9] 34.756 8.412 19.564 35.706 45.172
beta3_black[10] 28.938 9.520 19.371 24.355 45.408
beta3_black[11] 33.669 4.262 29.123 32.275 44.719
beta3_black[12] 32.913 0.567 31.714 32.964 33.808
beta3_black[13] 39.286 0.689 37.682 39.344 40.484
beta3_black[14] 38.128 3.664 30.303 38.449 45.243
beta3_black[15] 36.625 5.147 29.212 36.094 45.508
beta3_black[16] 33.690 4.136 29.111 32.410 43.399
beta4_black[1] -0.270 0.188 -0.637 -0.268 0.090
beta4_black[2] 0.280 0.173 -0.058 0.280 0.627
beta4_black[3] -0.992 0.178 -1.335 -0.992 -0.641
beta4_black[4] 0.625 0.212 0.216 0.623 1.049
beta4_black[5] -0.023 3.229 -6.324 -0.047 6.642
beta4_black[6] -0.018 3.130 -6.126 -0.021 6.031
beta4_black[7] -0.100 3.176 -6.496 -0.056 5.917
beta4_black[8] -0.835 0.368 -1.573 -0.824 -0.132
beta4_black[9] 2.114 1.080 0.230 2.018 4.534
beta4_black[10] 0.032 0.178 -0.330 0.034 0.382
beta4_black[11] -0.708 0.212 -1.131 -0.708 -0.303
beta4_black[12] 0.560 0.342 -0.101 0.554 1.248
beta4_black[13] -1.269 0.210 -1.683 -1.267 -0.867
beta4_black[14] -0.042 0.232 -0.495 -0.040 0.407
beta4_black[15] -0.933 0.210 -1.340 -0.936 -0.514
beta4_black[16] -0.597 0.232 -1.049 -0.595 -0.149
mu_beta0_black[1] 1.012 0.900 -0.928 1.088 2.463
mu_beta0_black[2] 1.314 0.655 0.050 1.352 2.312
mu_beta0_black[3] 1.957 1.181 -1.061 2.109 3.764
tau_beta0_black[1] 1.196 1.097 0.049 0.890 4.069
tau_beta0_black[2] 24.524 52.686 0.087 5.798 170.029
tau_beta0_black[3] 0.319 0.230 0.026 0.271 0.882
sigma_H[1] 0.225 0.047 0.140 0.223 0.330
sigma_H[2] 0.176 0.028 0.126 0.174 0.239
sigma_H[3] 0.186 0.041 0.114 0.183 0.274
sigma_H[4] 0.299 0.084 0.168 0.287 0.478
sigma_H[5] 1.019 0.216 0.634 1.007 1.474
sigma_H[6] 0.362 0.186 0.025 0.357 0.739
sigma_H[7] 0.292 0.058 0.199 0.285 0.429
sigma_H[8] 0.338 0.121 0.096 0.351 0.568
sigma_H[9] 0.527 0.128 0.330 0.511 0.822
sigma_H[10] 0.207 0.041 0.135 0.204 0.298
sigma_H[11] 0.270 0.045 0.196 0.266 0.372
sigma_H[12] 0.430 0.165 0.203 0.401 0.771
sigma_H[13] 0.218 0.038 0.151 0.215 0.300
sigma_H[14] 0.495 0.090 0.339 0.486 0.701
sigma_H[15] 0.248 0.039 0.182 0.245 0.338
sigma_H[16] 0.221 0.043 0.150 0.216 0.320
lambda_H[1] 3.573 5.010 0.173 1.941 17.718
lambda_H[2] 9.357 8.983 0.923 6.870 31.884
lambda_H[3] 6.224 8.584 0.303 3.368 30.038
lambda_H[4] 0.007 0.004 0.001 0.006 0.018
lambda_H[5] 2.248 6.053 0.018 0.428 18.112
lambda_H[6] 4.291 11.401 0.006 0.087 36.529
lambda_H[7] 0.016 0.011 0.003 0.013 0.046
lambda_H[8] 6.814 9.532 0.098 3.400 34.863
lambda_H[9] 0.016 0.011 0.003 0.014 0.045
lambda_H[10] 0.400 0.742 0.039 0.242 1.638
lambda_H[11] 0.266 0.474 0.011 0.120 1.377
lambda_H[12] 4.945 6.336 0.200 2.910 23.454
lambda_H[13] 3.782 3.452 0.206 2.804 12.944
lambda_H[14] 3.264 3.714 0.228 2.176 12.594
lambda_H[15] 0.024 0.034 0.003 0.016 0.094
lambda_H[16] 0.969 1.274 0.060 0.561 4.279
mu_lambda_H[1] 4.431 1.872 1.284 4.275 8.631
mu_lambda_H[2] 3.457 1.982 0.366 3.274 7.600
mu_lambda_H[3] 3.574 1.892 0.808 3.277 8.058
sigma_lambda_H[1] 8.720 4.198 2.149 8.080 18.206
sigma_lambda_H[2] 7.590 4.787 0.563 7.029 18.171
sigma_lambda_H[3] 6.373 4.011 1.077 5.483 16.297
beta_H[1,1] 6.975 1.036 4.514 7.116 8.580
beta_H[2,1] 9.883 0.467 8.891 9.914 10.748
beta_H[3,1] 8.009 0.730 6.252 8.100 9.244
beta_H[4,1] 10.543 7.658 -4.852 10.586 25.138
beta_H[5,1] -0.087 2.828 -5.700 -0.002 5.534
beta_H[6,1] 2.019 4.510 -7.845 2.871 8.622
beta_H[7,1] 1.744 5.392 -9.814 2.176 11.140
beta_H[8,1] 1.109 3.237 -3.025 1.168 3.571
beta_H[9,1] 13.297 5.406 2.851 13.274 24.535
beta_H[10,1] 7.233 1.529 4.037 7.288 10.027
beta_H[11,1] 4.862 3.606 -3.278 5.673 9.817
beta_H[12,1] 2.606 1.056 0.768 2.540 4.958
beta_H[13,1] 9.035 1.058 7.059 9.136 10.472
beta_H[14,1] 2.166 1.028 0.149 2.176 4.160
beta_H[15,1] -6.185 3.668 -12.909 -6.393 1.977
beta_H[16,1] 3.164 2.404 -0.919 2.929 8.739
beta_H[1,2] 7.932 0.245 7.459 7.930 8.407
beta_H[2,2] 10.044 0.128 9.796 10.045 10.297
beta_H[3,2] 8.972 0.189 8.592 8.974 9.341
beta_H[4,2] 3.307 1.469 0.470 3.284 6.167
beta_H[5,2] 1.927 1.002 -0.082 1.927 3.860
beta_H[6,2] 5.418 1.226 2.731 5.544 7.409
beta_H[7,2] 2.221 1.064 0.357 2.159 4.534
beta_H[8,2] 3.022 0.992 1.340 3.122 4.380
beta_H[9,2] 3.326 1.065 1.270 3.316 5.400
beta_H[10,2] 8.178 0.320 7.528 8.189 8.780
beta_H[11,2] 9.823 0.650 8.843 9.689 11.269
beta_H[12,2] 3.953 0.356 3.270 3.950 4.639
beta_H[13,2] 9.141 0.278 8.674 9.120 9.671
beta_H[14,2] 4.041 0.346 3.385 4.031 4.731
beta_H[15,2] 11.389 0.668 9.925 11.423 12.641
beta_H[16,2] 4.560 0.788 3.024 4.557 6.121
beta_H[1,3] 8.503 0.240 8.077 8.484 9.007
beta_H[2,3] 10.106 0.107 9.903 10.104 10.324
beta_H[3,3] 9.675 0.155 9.374 9.672 9.989
beta_H[4,3] -1.817 0.987 -3.593 -1.852 0.244
beta_H[5,3] 4.088 0.675 2.703 4.110 5.376
beta_H[6,3] 8.727 1.318 6.575 8.806 11.075
beta_H[7,3] -2.254 0.741 -3.782 -2.222 -0.876
beta_H[8,3] 5.404 0.514 4.695 5.327 6.437
beta_H[9,3] -2.550 0.733 -3.998 -2.535 -1.106
beta_H[10,3] 8.731 0.257 8.254 8.729 9.250
beta_H[11,3] 8.531 0.292 7.880 8.562 9.028
beta_H[12,3] 5.302 0.310 4.603 5.344 5.813
beta_H[13,3] 8.852 0.184 8.482 8.859 9.191
beta_H[14,3] 5.773 0.260 5.201 5.794 6.230
beta_H[15,3] 10.382 0.314 9.782 10.371 11.026
beta_H[16,3] 6.484 0.519 5.405 6.520 7.390
beta_H[1,4] 8.339 0.179 7.950 8.349 8.659
beta_H[2,4] 10.191 0.108 9.962 10.197 10.392
beta_H[3,4] 10.164 0.159 9.815 10.178 10.444
beta_H[4,4] 12.083 0.475 11.123 12.099 12.976
beta_H[5,4] 6.007 0.869 4.580 5.948 7.854
beta_H[6,4] 6.842 0.980 4.842 6.936 8.337
beta_H[7,4] 8.114 0.346 7.414 8.117 8.793
beta_H[8,4] 6.880 0.322 6.352 6.848 7.575
beta_H[9,4] 7.188 0.469 6.269 7.187 8.104
beta_H[10,4] 7.871 0.236 7.432 7.857 8.372
beta_H[11,4] 9.409 0.196 9.034 9.406 9.801
beta_H[12,4] 7.164 0.210 6.761 7.161 7.606
beta_H[13,4] 9.089 0.147 8.810 9.086 9.369
beta_H[14,4] 7.774 0.213 7.362 7.767 8.212
beta_H[15,4] 9.517 0.235 9.052 9.518 9.969
beta_H[16,4] 9.324 0.216 8.940 9.311 9.786
beta_H[1,5] 9.007 0.147 8.707 9.010 9.288
beta_H[2,5] 10.791 0.091 10.611 10.788 10.977
beta_H[3,5] 10.927 0.166 10.624 10.918 11.289
beta_H[4,5] 8.479 0.369 7.722 8.488 9.198
beta_H[5,5] 5.265 0.725 3.582 5.363 6.440
beta_H[6,5] 9.001 0.670 7.972 8.890 10.491
beta_H[7,5] 6.876 0.330 6.235 6.872 7.517
beta_H[8,5] 8.257 0.194 7.905 8.250 8.632
beta_H[9,5] 8.220 0.489 7.228 8.227 9.185
beta_H[10,5] 9.998 0.221 9.536 10.002 10.418
beta_H[11,5] 11.495 0.223 11.050 11.500 11.932
beta_H[12,5] 8.484 0.193 8.089 8.481 8.858
beta_H[13,5] 10.017 0.131 9.762 10.016 10.272
beta_H[14,5] 9.213 0.223 8.808 9.198 9.679
beta_H[15,5] 11.155 0.249 10.663 11.158 11.654
beta_H[16,5] 9.917 0.171 9.573 9.921 10.245
beta_H[1,6] 10.169 0.192 9.847 10.158 10.606
beta_H[2,6] 11.503 0.105 11.303 11.500 11.720
beta_H[3,6] 10.809 0.158 10.467 10.815 11.089
beta_H[4,6] 12.745 0.637 11.524 12.725 14.036
beta_H[5,6] 5.957 0.719 4.677 5.921 7.419
beta_H[6,6] 8.548 0.767 6.623 8.704 9.653
beta_H[7,6] 9.743 0.544 8.682 9.739 10.818
beta_H[8,6] 9.486 0.250 9.027 9.498 9.909
beta_H[9,6] 8.438 0.805 6.880 8.423 10.056
beta_H[10,6] 9.582 0.291 8.932 9.608 10.084
beta_H[11,6] 10.829 0.345 10.078 10.854 11.445
beta_H[12,6] 9.366 0.245 8.913 9.354 9.908
beta_H[13,6] 11.046 0.172 10.757 11.033 11.405
beta_H[14,6] 9.823 0.284 9.257 9.830 10.365
beta_H[15,6] 10.850 0.432 9.999 10.845 11.680
beta_H[16,6] 10.550 0.223 10.062 10.561 10.950
beta_H[1,7] 10.922 0.844 8.869 11.008 12.313
beta_H[2,7] 12.196 0.413 11.379 12.196 13.014
beta_H[3,7] 10.553 0.626 9.177 10.607 11.655
beta_H[4,7] 2.853 3.205 -3.784 2.867 9.086
beta_H[5,7] 6.640 2.424 2.431 6.442 12.133
beta_H[6,7] 9.668 2.920 4.282 9.443 16.977
beta_H[7,7] 10.992 2.699 5.685 11.008 16.325
beta_H[8,7] 10.924 0.966 9.431 10.863 12.758
beta_H[9,7] 4.593 4.019 -3.455 4.683 12.444
beta_H[10,7] 9.714 1.345 7.217 9.649 12.641
beta_H[11,7] 11.038 1.704 7.859 10.939 14.702
beta_H[12,7] 9.982 0.893 7.990 10.060 11.510
beta_H[13,7] 11.639 0.808 9.759 11.753 12.826
beta_H[14,7] 10.378 0.927 8.446 10.410 12.099
beta_H[15,7] 12.076 2.254 7.673 12.130 16.456
beta_H[16,7] 12.229 1.192 10.359 12.068 15.074
beta0_H[1] 8.566 12.639 -18.514 8.674 33.931
beta0_H[2] 10.566 6.002 -1.055 10.642 22.664
beta0_H[3] 9.934 9.417 -8.003 9.838 30.049
beta0_H[4] 2.405 178.901 -375.399 5.863 371.052
beta0_H[5] 5.065 33.025 -58.790 4.397 72.839
beta0_H[6] 7.094 65.992 -133.060 7.214 149.907
beta0_H[7] 8.237 116.831 -229.015 9.473 243.654
beta0_H[8] 6.593 29.415 -18.589 6.392 35.133
beta0_H[9] 9.617 115.157 -226.761 10.302 237.158
beta0_H[10] 8.941 30.645 -57.636 9.688 70.422
beta0_H[11] 9.461 53.033 -103.646 9.958 114.899
beta0_H[12] 6.679 12.602 -15.537 6.433 31.508
beta0_H[13] 9.831 12.579 -8.722 9.667 30.921
beta0_H[14] 7.008 11.790 -16.285 7.046 27.954
beta0_H[15] 11.320 111.577 -222.649 11.029 229.968
beta0_H[16] 8.482 22.526 -36.337 8.291 53.604